Human death came as a result of the Fall, not necessarily the death of other living things. The key is to remember that the sin of Adam and Eve brought evil into the physical world. Moral evil is the main thing we are talking about there, but "physical evil" is also included.
Death, disease, aging, natural disasters, thorns and thistles, these are physical evils when they negatively affect human beings. Logically, we must have been preserved from their effects before the Fall. But the deaths of plants and of non-human animals are not evil unless they negatively affect human beings, for whose sake they were created. Indeed, the death of a non-human animal or plant can be a good thing when it in some way helps people. Death in this case has nothing evil about it; it is just a flux of matter and energy. There is no reason, therefore, to hold that physical death did not affect these things prior to the Fall, indeed it is nearly impossible to imagine how the world could have functioned without it.
Regarding the seven (really six, since the seventh was a day of rest) days of creation, I would hesitate to call them phases of natural history.
Certainly it is interesting when scientists find out something that fits curiously well with the account in Genesis, such as the existence of light before the first stars, which to earlier generations seemed absurd. It is possible that God providentially guided Hebrew mythology to reflect actual natural history on some points. Fundamentally though, we should not expect God to reveal scientific matters to ancient peoples. Genesis should instead be interpreted as an inspired and authentically theological mythology, in the very positive sense of that word. Nothing in the account is false. Indeed it is all the word of God. But it expresses truths about the universe through the genre of mythology.
Most importantly, the account emphasizes how everything in the universe has its origin in God, and by implication that God transcends the universe and has ultimate power over it. Anthropologists have noted many similarities in details to the mythologies and cosmologies of neighboring peoples, especially those of Mesopotamia where the Bible says Abraham and Sarah were from, but these details are reworked into an entirely different ultimate view of the universe.
I would view the actual six days of creation as atemporal aspects of God's creation of the universe rather than successive epochs of the distant past. Though science can now explain the creation of light before the creation of the sun, moon, and stars, ancient Semitic people presumably would not have known about this and so the separation of them suggests that even the original Israelites did not take the story in a "fundamentalist" way. The difficulty of reconciling this first creation story with the second is another piece of evidence for this. Surely whoever first put them next to each other was intelligent enough to notice that they do not match up if interpreted with block-headed "literalism." The evenings and mornings which pass before the creation of the sun could also be interpreted as supporting a more poetic meaning.
Anyway, what is still irreconcilable with the modern scientific account of the past is the creation of birds before that of land animals. Therefore instead of epochs of history I would view the six days as systematic classification of the universe and a statement that God created all of it.
We begin with nothing but waters (representing primeval chaos- the lack of any kind of order or distinctions) and the Spirit of God.
Then God acts:
First, he makes the fundamental distinction between light and dark, which can be taken literally, or allegorically as representing truth and falsehood, good and evil, being and non-being, etc. It is the light he actually creates, while the darkness is a mere absence of light.
Second comes the distinction between the waters below the sky and the "waters" above the sky. This is more awkward according to modern scientific cosmology, but it was an important distinction to make for ancient Semites.
Third comes the distinction between sea and land. Since the sea represented untamed, unformed chaos to the Semitic mind, this is imagined as creating the land and separating it from a pre-existing sea. Interestingly, plant life is seen as a part of the land.
Next comes the creation of the creatures associated with these three great dichotomies of Creation.
First, the sun, moon, and stars, creatures of light corresponding to the first day in which light was created and separated from the darkness and "ruling" the day and night.
Second, the fish and birds are made, corresponding to the sea and sky which were distinguished from each other on the second day.
Third, corresponding to the land and its separation from the sea on the third day, the inhabitants of the earth are created- land animals and man. Man is then given a sort of mastery over the whole.
Finally God rests, a reflection of the Jewish Sabbath and for us Christians a very mysterious and profound idea, the kind of soil from which mysticism springs (though the same could be said for the clarity of the previous six days- mysticism need not be mysterious).
Anyway, that's my view on the subject. It is certainly a difficult one, and one on which a wide variety of positions are tolerated in the Church.